help-0

[rotund plank]

so if you think of the ladder as a straight line I meant that it didn’t seem immediate that the ladder couldn’t be slanted over the box

as opposed to perpendicular to the horizontal edges of the box

this makes sense though, so you’re saying this is just an assumption I should make in a problem like this

[ancient saddle]

Yes, at least by now. In the future the problems might be more realistic or have more details

[rotund plank]

yep that makes sense

and given it’s homogenous in that way it immediately reduces to 2D

thanks a lot for the help!

[ancient saddle]

Great, you're welcome 👍🏽

[rotund plank]

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[solid spruce]

i thought fundamental was just AND, OR, NOT

no idea which to choose from this list...

[oak turret]

i guess the last one then?

since it contains and, or, not

ive never heard the term fundamental boolean operator

[solid spruce]

oh i think you're right

i was thinking too much into it when itwas just 'contains'

ty

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[mighty crest]

is it u sub

and if so what should i sub it with

im guessing sec

cuz du of sec is tan x sec x

correct me if im wrong

ims tuck

stuck

[solemn juniper]

your du is wrong, the argument of the functions should be 3x

but otherwise you have the right idea

[mighty crest]

ah i see

[solemn juniper]

better

[mighty crest]

but what happens now

du = 3 sec 3x tan 3x dx

[solemn juniper]

you need a sec3x left in the integral

[mighty crest]

no because i subbed

it

with u

[solemn juniper]

your initial integrand is tan3x*sec^5(3x)

[mighty crest]

yes\

[solemn juniper]

you need a tan3x*sec3x for your du. What does that leave you with?

[mighty crest]

i dont get it

if i wanted to write everything in terms of u

how would that work

[solemn juniper]

i'm saying you can't turn sec^5(3x) into u^5 because you need to keep a sec3x left over when you sub out dx

[mighty crest]

like this

[solemn juniper]

much better

[mighty crest]

got it

I got trouble isolating my dx

idk why

[solemn juniper]

a lot of these trig integrals will involve factoring part of the integrand to make things line up

[mighty crest]

ye the goal is to make everything cancel out

[solemn juniper]

so it's a good strategy to keep in mind

[mighty crest]

I will keep that in mind

[solemn juniper]

[mighty crest]

i got the answer wrong

mine is 3x

while the book is sec^5 x

[mighty crest]

u have an idea about what i did wrong

[solemn juniper]

yep

[mighty crest]

thats the book

ah the book is wrong

[solemn juniper]

indeed

[mighty crest]

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[worldly bolt]

I have no idea what to do here

[worldly bolt]

I think I'm supposed to do something with a circle formula?

π r^2

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[chilly idol]

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[waxen owl]

Can I do substitution on this

I’m trying

[lone heart]

@waxen owl Has your question been resolved?

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[winter kettle]

a, b, c is a geometric sequence. their sum is 7 and multiple is 8. find the greatest number out of the three

[tribal valve]

its a really simple one, try thinking of it in your mind

[winter kettle]

wait

im so dumb

1,2,4

[tribal valve]

👏

[winter kettle]

ok wait 😭

how would i solve it algebraically?

a+b+c=7
abc=8

[tribal valve]

yeah

i mean

you can't

3 variables

2 equations

[winter kettle]

its not possible?

even with like

substitution methods

ex. a x b x c = a * a * r * a * r^2

[tribal valve]

what math are you in?

[winter kettle]

calc

but i didnt learn sequences properly 🫠

[tribal valve]

bc?

[winter kettle]

ab

[tribal valve]

huh

sequecnes and series are usually bc stuff

[winter kettle]

oh

[tribal valve]

give me a second i'm thinking

ah

found it

i think

represent b and c in terms of a

[winter kettle]

geometrically or arithmetically? or both

[tribal valve]

algebriaclly

[winter kettle]

sorry *arithmetically

[tribal valve]

its an geometric sequence

so

[winter kettle]

i tried? both

for geo i ended up getting a^3 + r^3 = 8

[tribal valve]

this is what i was trying to say 😭

[winter kettle]

and then i didnt know where to go from there

[tribal valve]

right

wait

ok

let me restart my explanation

what is a * b * c

[winter kettle]

i just ended up repeating steps😭 *replace r^2 for r^3
manual typo

[winter kettle]

8

[tribal valve]

yes

write abc in terms of a and r

[winter kettle]

a^3 * r^3?

[tribal valve]

yes

so $a^3r^3 = 8$

[ocean seal]

dabbingpotato

[tribal valve]

now sum

what is a+b+c

[winter kettle]

in terms of a and d (d= common diff), 7= 3a + 3d

[tribal valve]

its geometric

you should be able to represent it in terms of a and r

[winter kettle]

o uh
a + (ar) + (ar^2) ?

[tribal valve]

yep

what is that equal to

[winter kettle]

a + (ar) + (ar^2) =7

[tribal valve]

yep

now you have a system of equations

2 variables

2 equations

its solvable

[winter kettle]

ohh

hold on ill try

[tribal valve]

might be messy

but gl

[winter kettle]

thank you

.close

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[lone heart]

@solid fog Has your question been resolved?

[solid fog]

oh wrong picture

[drifting seal]

I would like to simplify f(x) first

wait

it cannot be factorize, lol

[drifting seal]

little wrong

[solid fog]

yeah ik

I tried different ways

im confused

[drifting seal]

this is correct?

[left isle]

yeah it is

[drifting seal]

Then what's ur question?

!status

[lone heart]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[left isle]

the last part should be 12/(x+8), not 92

[drifting seal]

ys, and it's -8x too

[left isle]

also you have a 9x in your answer

yea

[solid fog]

sorry

im confused on why its wrong

[drifting seal]

12/x+8 bruh

not 92

[drifting seal]

U do this right?

[solid fog]

i did it yea

but it doesn't make sense

..

[left isle]

should be a +12 shouldn't it?

[solid fog]

why +12?

[left isle]

oh oops i read it wrong

[drifting seal]

Wait I have a thinking of

f(x) / g(x) is not equal to f/g (x) ???

idk

WAIT

I look wrong lol

it was -9

not 9, lol

[left isle]

oh yep

that'll do it

[solid fog]

thank you @drifting seal @left isle

it was right btw forgot to tell yall

I see what i did wrong now

.close

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[oak matrix]

How do you put this in matrix form?

[woven moon]

What do you get when you evaluate a b c x1 (d e f) (x2) g h i x3?

[oak matrix]

What

[woven moon]

That's meant to be a 3x3 matrix multiplied by a 3-vector

[oak matrix]

Wait I’m confused are you asking a question or answering my question

[quick halo]

have you tried simplifying those equations

[woven moon]

Work it out, then you can fill in the blanks

it will help you understand

[oak matrix]

How do you simplify them?

[quick halo]

Using algebra

and subtracting things from both sides, collecting like terms, and things like that

[oak matrix]

You’re allowed to do that? I thought you have to represent the entire thing

[woven moon]

You can do that if you're trying to solve it, but it won't help you put it into matrix form

[oak matrix]

Like this?

Sorry I just started learning about them today I feel like I don’t understand anything

[woven moon]

like this

[woven moon]

That's fine

When you put equations like that into matrix form, it means putting it into the form x1 x1 (x2) = A (x2) x3 x3

where A is a 3x3 matrix

[oak matrix]

So like this then?

The circled*

[woven moon]

Yeah that looks good

It makes it easier to do things with it if you write it as a 3x3 matrix though

[oak matrix]

I just don’t get how they would look on the other side

[woven moon]

so the 3rd column would be all 0s

[oak matrix]

Is it just x1 x2 x3 as like a column

[oak matrix]

Ohhh I see ok

[woven moon]

yes

if x is the column vector x1 x2 x3, and A is a 3x3 matrix, then you would write it as x = Ax

then when you look at each row, you get back the original equations

does that make sense?

[oak matrix]

I think so

Tysm

❤️

[woven moon]

It looks complicated, but for bigger systems it actually makes things easier

so stick with it

[oak matrix]

I will tyyyy

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[alpine sable]

can someone help me understand this

[red sinew]

have you tried writing it all as a table?

[alpine sable]

idk if im allowed to do that on the test

i have to use the laws

[red sinew]

which laws could you use here?

[woven moon]

Do you know what all the symbols mean?

[alpine sable]

not and or

yes

[alpine sable]

this is a bit diff than the one given to me

[woven moon]

Are you trying to show that the left is equal to the right, or just to understand why it's true?

[alpine sable]

im supposed to verify

using the laws

[woven moon]

Yeah so like they did there, it's normally easiest to start from the middle and use laws to remove terms

[alpine sable]

look at the negation law

not p and t makes not p?

[woven moon]

t means true I think

p ^ t is equivalent to p

so yes

[alpine sable]

taoutology

tautology

[woven moon]

yeah same thing

does it make sense?

(you're right, tautology is more precise)

[alpine sable]

how tf does that turn into that

q and not q = not q?

false and not false = false

makes sense

wait no it doesnt i messed up

[woven moon]

the distributive law says that (P ^ Q) v (P ^ R) == P ^ (Q v R)

[alpine sable]

right

[woven moon]

in this case P = ¬p, Q = q, and R = ¬q

[alpine sable]

shii dude i'd literally buy you a 20$ mic if u could help me out ahaha

[woven moon]

lol

sorry

[alpine sable]

makes sense

but u want that?

[woven moon]

I acc can't tell if you're joking but no thanks

Most of those laws make sense once you've thought them through, so they're not too bad to memorise

[alpine sable]

i have a quiz on monday

and i know when its a law

but i cant tell which one is which

[woven moon]

wdym, you can't remember which names go with which laws?

[alpine sable]

yes

like if i see a distributive law i can tell its a law

cuz intuitively it makes sense

but i cant tell its a distributive law

[woven moon]

that's just a matter of memorising the table unfortunately

that one in particular does make sense though

if you replace ^ with multiplication, and v with addition, you get the normal distributive law

and they distribute over each other so you don't need to memorise which way round it is

[alpine sable]

this makes sense

but how does

not p and t equal to p

sorry typo

[woven moon]

not p and t is equal to not p

[alpine sable]

imma do a truth table rq

[woven moon]

yeah good idea

it is also one of the identity laws

[alpine sable]

yeh it checks out bahaha

give me a scenerio which this is the case

so i can better understand it

[woven moon]

wdym, a scenario where ¬p^t = ¬p?

ig the first usage that comes to mind is if you're trying to apply a theorem that requires two things to be true, but you already know that one of them is true

[alpine sable]

yes

[woven moon]

so you only need to show the second thing

that's the intuition behind the law

[alpine sable]

right

but can u give me a scenerio

also how do u do the not sign

[woven moon]

shift + backtick (`)

[alpine sable]

~p

not the same LOL

[woven moon]

you can also use that, they're both used

[alpine sable]

okie

i cant think of a scnerio for this

[woven moon]

let's say you know that d is a divisor of xy, and you know that euclid's lemma says that if p is a prime divisor of ab, then p|a or p|b

if you wanted to show that d|x or d|y, then one way to do it would be to apply euclid's lemma

so you'd need to show that (a) d is prime, and (b) that d|xy

but you already know that d|xy, so you can replace that with true

(also side note: that is the difference between a tautology and truth)

then you can use that identity law to show that

(d is prime) ^ (d|xy) = (d is prime) ^ (true)
= (d is prime)

so you only need to show that d is prime

does that make sense?

that's basically what that law is saying

[alpine sable]

yes kinda

thank you

im gonna solve this and send

lemme know if im right

[woven moon]

sure

[alpine sable]

i hope you can read it my guy ahaha

i fucked up

idk where i fucked up

[woven moon]

I don't think you did

what does the answer say?

[alpine sable]

no asnwer

i fucked up idk

[woven moon]

cos I got the same as you, r v q

oh no I misread

[alpine sable]

i got

p v ( r v q)

[woven moon]

yeah that's not right then

one sec

it was right until the last line

everything on that piece of paper is right

so you've got (p v q) ^ (r ^ q)

[alpine sable]

yes then after that

im fucked

[woven moon]

where do you go from there?

[alpine sable]

excuse my language btw

[woven moon]

alright think about it this way

also dw I'm a uni student so idc lol

[alpine sable]

i have no idea but it looks like associative law

[woven moon]

if (r^q) is true then r is true, and q is true

this is just intuitive btw, you have to do it formally

but if that's the case, what can you say about (p v q)?

[alpine sable]

thats also true

[woven moon]

good

[alpine sable]

so its a tautology?

[woven moon]

yes

so what's the answer?

[alpine sable]

dont know

:/

[woven moon]

you've worked out that (p v q) is a tautology so we can replace it with t

so how do you simplify t ^ (r ^ q)?

[alpine sable]

associative?

[woven moon]

you can do that

so you get (t ^ r) ^ q

is there a way of getting rid of the t?

[alpine sable]

r?

r ^ q?

[woven moon]

exactly. that's the answer, so you know what you're aiming for

[woven moon]

but now you have to show it properly from here

[alpine sable]

appreciate it brother

wait wht was ur major again?

also i added if u dont mind ahaha

[woven moon]

I do math but I've done logic before

np

[woven moon]

if I'm being honest idk how to explain how you get rid of the first term formally, other than just saying you build an intuition over time

I'll give you a clue: try using absorption

[woven moon]

I take it you're 1st year cs?

[alpine sable]

yes

finished my gen ed

2nd year

[woven moon]

nice

[woven moon]

have you made any progress?

[alpine sable]

im working with a tutor from tutor.com rn

but hes english isnt the best

we're just laughing ahahaha

[woven moon]

lol

[alpine sable]

im getting it though

[woven moon]

I gtg now but here's the solution if you want it:

||(p v q) ^ (r ^ q) = (p v q) ^ (q ^ r) (commutativity)||
||= ((p v q) ^ q) ^ r (associativity)||
||= (q ^ (q v p)) ^ r (commutativity -- this may not be necessary though, it depends on how anal the person marking is)||
||= (q) ^ r = q ^ r (absorption)||

good luck with your test

[lone heart]

@alpine sable Has your question been resolved?

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[solid arch]

Can someone confirm if this is the correct answer?

[solid arch]

It’s a rational equation

[quick halo]

You can check your answer by substituting back in

[sour dove]

It all looks fine until this part right here. That factoring is not correct

[lone heart]

@solid arch Has your question been resolved?

[keen thicket]

I think you should spilt it first[the middle term]

Not direct

Just to be sure

Check it with alpha and beta

Alpha= R1, Beta = R2

Alpha + Beta = -b/a
Alpha × Beta = c/a

@solid arch

3+(-2)=-(-1)/2
1=1

3×(-2)=-6/2
-6,-3
I don't think it's correct with Aplha Beta

Alpha*

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[scenic wing]

im stuck on 136

[scenic wing]

i know the denom cant be 2

x cannot equal 2 i mean

[atomic harbor]

Yes and what type of discontinuity it is?

[scenic wing]

so since it has absolute value its jump discontinuity

[atomic harbor]

Yeah right

[scenic wing]

???

[atomic harbor]

It's discontinues at some other point as well?

[scenic wing]

-1 and 1

[atomic harbor]

How?

It's well defined on those two points

[scenic wing]

i dont know then

[atomic harbor]

Yeah there is no discontinuity apart from x= 2

[pulsar spire]

if it cant equal 2, what point should it pass over

[scenic wing]

ok you said there was more

[atomic harbor]

I was just asking should there be any other discontinuity apart from x=2? Expecting no as reply

[scenic wing]

how do i know what type of discontinuity this is

so its one point so its a hole discon ?

[pulsar spire]

yea i believe so

[atomic harbor]

Yes, it's a removable (hole) discontinuity but not becuase f(x) is discontinues at only point, it's because the discontinuity is of the form 0/0

[scenic wing]

what do you mean 0/0

ok the final answer

[atomic harbor]

You get 0/0 if you evaluate f(1)

[scenic wing]

ok

and

[gray isle]

consider factorisation

0/0 doesn't automatically mean hole

[lone heart]

@scenic wing Has your question been resolved?

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[slate matrix]

my eigen values for a is -1,6 but for a-1 im getting 1/6 and 2/3

am i going wrong somewhere?

[lone heart]

@slate matrix Has your question been resolved?

[tardy stag]

,w eigenvalues of inverse of [[1,-2],[-5,4]]

[ocean seal]

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Requested by kitten.in.a.teacup

[tardy stag]

it would appear you are

@slate matrix ^

[slate matrix]

okay thank you

.close

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[peak lake]

Hi I just need help with someone just explaining how to do this

[peak lake]

I don’t understand

It

[sour dove]

it's asking you to basically figure out what the square root equivalent for each value is. You basically have to square the value then wrap them up in a sqrt. Make sure you convert before hand (for example, re-write 0.9 as 9/10

For example, $5 = \sqrt{25}$

[ocean seal]

MellowDramaLlama

[peak lake]

And so 7 n 49??

[sour dove]

yep!

[peak lake]

And for uh the cube root

5x5x5 ??

[sour dove]

yep! So the equivalent would be $\sqrt[3]{125}$

[ocean seal]

MellowDramaLlama

[peak lake]

Thank you!! Yeah it would definitely be easier if it was worded like that

[quartz mica]

it's just asking what number that rooted is that number

so basically just power it

and put a root over it

[peak lake]

Thank youu

.close

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[carmine tiger]

Can correct me

I wanna know if it’s right or not if it’s wrong please circle the right answer in green for me please

[quartz mica]

nope, unfortunately incorrect

[carmine tiger]

Can give me the right answer

[quartz mica]

should be B

[carmine tiger]

Daim idk what I did wrong

[quartz mica]

-10-10=-20

what r u doing

[carmine tiger]

I put 8 on the far right and then did 14+8

For the first question

[quartz mica]

first question should be B

-14+14=0

[carmine tiger]

Oh

[quartz mica]

you should eliminate terms to 0

simplify

[carmine tiger]

Oh ok

[quartz mica]

think it like this

you move the terms from one side to another

and they change + to -

or - to +

[carmine tiger]

Yep

If it’s + we change to - and if it’s - we change to +

[quartz mica]

for the second question, should be C

(7k-3+3)/7=k

since 7k/7=k

and third question is B

said prior

[carmine tiger]

Oh

[alpine sable]

ah so i am dumb and i dont know how to find root of improper numbers
please help me
im tried tricks on ytube but they give approx answer 437.5 but we are supposed to get the answer as 434

[carmine tiger]

What about the 4 question how do I do it

[alpine sable]

are u talking to me?

[carmine tiger]

Nope srry

[quick halo]

this help channel is occupied, please go to an available one like #help-25

[alpine sable]

ok

[carmine tiger]

Yow

.close

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[wary finch]

i have an little problem that im not sure if im correct or not

[wary finch]

but there is another problem that im french so the problem is with french sentence

oh wait im a idiot

i just need to translate

[carmine tiger]

.reopen

[wary finch]

"I climb a mecanic stair, when he off, i climb it to 4 minutes
"when that stair is on, i climb it to 2 minutes
"how many times it's take when the stair is on while i walk

ps : i tried my best to translate so im sorry if i made some mistake (im in key stage 5)

[quick halo]

can you go to an available help channel like #help-36

[quick halo]

my understanding of your problem is like this:
there is an escalator. When it is off, it takes 2 minutes to climb it. When it is going down, it takes 4 minutes to climb it. WHen it is going up, how long does it take to climb it?

[wary finch]

off -> 4 minutes to climb it
on -> 2 minutes to climb it
on + climbing -> ???

looks like this

[quick halo]

oh

[quick halo]

consider rates

[wary finch]

ah

[vale wigeon]

from what language?

[wary finch]

french, i translate french to english

for me he takes 1 minute to climb it while escalator is on

[vale wigeon]

show the original french

[wary finch]

ok

"Je monte un escalier mécanique à l'arrêt en quatre minutes."
"Lorsque cet escalier fonctionne et que je reste immobile je monte celui-ci en deux minutes."
"Combien de temps dure la montée si je monte cet escalier mécanique lorsqu'il fonctionne ?'

done

[vale wigeon]

ok

alors quand on monte on couvre 1/4 de l'escalier par minute

et l'escalier fonctionnant lui-même courve 1/2 de l'escalier par minute

[wary finch]

oh ok

[lone heart]

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[cerulean talon]

need help on b)

[fallow sky]

3 energy jolts is the answer

[cerulean talon]

what?

i don’t think so..

[fallow sky]

p = e2mc^2

[cerulean talon]

huh?

<@&286206848099549185>

[fallow sky]

the cartographic value scale

[cerulean talon]

bro idfk what you’re talking about but i know it’s not related to my question

[sullen rain]

I think he's trolling.

[cerulean talon]

yeah

[agile wind]

Bro

[cerulean talon]

<@&268886789983436800>

[agile wind]

We got 0.17

In first one right

[cerulean talon]

yeah?

[agile wind]

Approx

1.6772

So we multiplied

[cerulean talon]

wait 0.17

[violet hemlock]

dealt with

[agile wind]

1.6 mass

[tardy stag]

put units on your answers

[cerulean talon]

thank you

[cerulean talon]

i’m sorry

[cerulean talon]

ok yeah

[agile wind]

Did u understand

[cerulean talon]

but the velocity

we take from first part

1.7

[agile wind]

0.17

[cerulean talon]

what? why?

[agile wind]

I did the math and I got this

@cerulean talon

[cerulean talon]

wait but what i got

2.659456 is right

but the part after

idk what to do

see on b?

i see what you mean on a tho..

oh

i see what you mean

okay

0.265945946

now what i do?

[agile wind]

That's

Final momentun

Final - initial

[cerulean talon]

oh okay

so i get 0.099729730

then what u do?

@agile wind

[agile wind]

,calc 0.2656 - 0.32

[ocean seal]

Result:

-0.0544

[agile wind]

@cerulean talon

[cerulean talon]

where’s -0.32 from?

@agile wind

[agile wind]

Initial momentum

Like before eating small fish

We are taking only big fish momentum not small one included

@cerulean talon

[cerulean talon]

wait so

i see

i get it now, thanks

.close

[lone heart]

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[alpine sable]

The lateral side of an isosceles trapezoid is equal to 25 cm, height - 20 cm, and the middle line is 33 cm. Find the lengths of the bases of the trapezoid.

[alpine sable]

.close

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[small timber]

I don't understand how I have to solve this

[quick halo]

You can start by letting the principal amount be P

then you can use the compound interest formulas to get an equation for P

[small timber]

Is it like this?

I don't understand how to actually do it so I calculated and idkk

[quick halo]

,rotate

[small timber]

which one is the correct one? the one on the left or the right

[quick halo]

I think right side is closer, but you have to remember to do it over 9 years instead of over 9 quarters

[small timber]

27/12=2.25 x 4 = 9

how i got the 9

[quick halo]

ohh

sorry

then right side is right

[small timber]

ohh okayy tqq

[lone heart]

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[rocky pewter]

can you please help me to continue/correct the green theorem ?

[lone heart]

@rocky pewter Has your question been resolved?

[rocky pewter]

<@&286206848099549185>

[lone heart]

@rocky pewter Has your question been resolved?

[lone heart]

@rocky pewter Has your question been resolved?

[lone heart]

@rocky pewter Has your question been resolved?

[rocky pewter]

could you repeat please?

[rough sphinx]

i think im in the wrong chat

[ancient saddle]

The bounds for x are incorrect. You should get them from x²=4

Also what happened to 2x-3 in the double integral? 🤔 Those steps are confusing

[lone heart]

@rocky pewter Has your question been resolved?

[errant agate]

I need help
Function= x^2-3
I need to find vertex, axis of symmetry, y, x intercepts, increasing and decreasing intervals with notation

[lone heart]

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[violet stream]

How do I find the range? I understand that they all have a range and what type for the parent function but how do I add find the range of f

[tacit arch]

Range is all possible y values

Can y be zero?

Can y be 1?

Basically keep asking yourself different numbers until you find a pattern

[violet stream]

I don't fully understand

I don't really know how to ask what I don't understand though

is y 0?

and how would that be written

y≤1?

or something different

wait

is it y ≤ 0?

@tacit arch

[violet stream]

Because at the max height that it is at it is at 0 so I feel like that makes sense

[tacit arch]

This is right

[violet stream]

Okay

If it was one up and to the left(the corner spot) would it just be y≤1?

then the domain is all real numbers

[lone heart]

@violet stream Has your question been resolved?

[violet stream]

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[gentle berry]

what's the question

I may or may not be able to help.

[violet stream]

it's pretty simple so probably

[violet stream]

.

[violet stream]

Based on this picture

[violet stream]

.

[gentle berry]

oh is this it? you want the range?

[violet stream]

no I found out the range from the other helper

I just need to make sure it wasn't a lucky guess and I'm doing it correctly

[gentle berry]

OK

range is all possible y values the graph takes on

or in other words, the y values the "graph" or "curve" touches

[violet stream]

ah

[gentle berry]

so what would the range of this be

[violet stream]

hmm

y ≤ -1?

[gentle berry]

start from the bottom and go to the top

what's the lowest value

[violet stream]

-5

[gentle berry]

and highest?

[violet stream]

-1

[gentle berry]

boom it's [-5,-1] or $-5\leq y \leq-1$

[ocean seal]

JayRoc (The Hurricane Panda)

[violet stream]

oh

I haven't learned the full shapes yet

but thanks for the future stuff when I do you t

[gentle berry]

it's ok. the nice thing about the ranges on graphs is that you can just look at the graph for the most part and figure out what it is

but my above notation just says

that y is between -5 and -1 inclusive

[violet stream]

If this was a half circle (only including the top half) would it have been y≤-1?

[gentle berry]

not necessarily

let's see

how about this one?

[violet stream]

hmm

[gentle berry]

start from the bottom and go to the top

[violet stream]

wait is there a different formula for circle shapes vs the corner shapes in my picture

?

[gentle berry]

yup

your function is defined as y=|x| (parent function) and the circle is generally x^2 +y^2=r^2

this one specifically is x^2+y^2=4

[violet stream]

oh yeah I haven't learned this far either 😅

[gentle berry]

it's ok, you're doing ranges tho right?

[violet stream]

I learned a few different parent functions

[gentle berry]

we can work with those

how about this one

[violet stream]

these

[violet stream]

Y ≥ 2?

[gentle berry]

yup you got it

[violet stream]

Okay

[violet stream]

Can you show me how to do these parent functions

@gentle berry

Other than the third one because that's the one we did

[gentle berry]

how bout this one?

[violet stream]

hmm

I kinda forgot the other range parent functions so sorry if I don't know some of them

hmm

uh

[gentle berry]

don't memorize it for each one

let the picture guide you

lowest value

[violet stream]

y ≥ -7?

[gentle berry]

ya there ya go

[violet stream]

okay cool

[gentle berry]

and this?

[violet stream]

y ≤ -7?

[gentle berry]

perfect

ranges don't change for lines. how about this one?

[violet stream]

is it all real numbers?

[gentle berry]

⭐

ez

that's true for ALL lines/linear equations

[violet stream]

I understand what all real numbers now

[violet stream]

Ah

So it'd be the same for the last parent function?

[gentle berry]

that's right

straight lines

slanted

they all the same

[violet stream]

okay thanks so much hopefully I can pass the quiz

[gentle berry]

yeh np

only word of caution

is this

idk how far along in algebra you are but in case you're given somethin like this

where the line doesn't stretch across the screen

just let the picture guide you

[violet stream]

y ≥ 1.5?

and no I don't think I'm that far

[gentle berry]

you're real close. I know you can't see it, but it's at 1

but ya u got it

[violet stream]

But once I am I'll remember this

[violet stream]

Ah okay

[gentle berry]

ya there ya go 😄

[violet stream]

thanks! time to sleep lol

[gentle berry]

jay gonna float around like a free particle now. night!

[violet stream]

cya thanks for the help

.close

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[mystic fern]

How can I find the tangent line?

[sour dove]

I'm assuming derivatives are fair game?

[mystic fern]

yes?

<@&286206848099549185>

[opal stone]

To find the equation of the tangent line to the curve represented by the function y = (x + 2)/(x - 3) at the point (2, -4), you can follow these steps:

Calculate the derivative of the function y = (x + 2)/(x - 3) to find the slope of the tangent line. Use the quotient rule for differentiation:

y' = [(x - 3)(1) - (x + 2)(1)] / (x - 3)^2

Simplify the derivative:

y' = (x - 3 - x - 2) / (x - 3)^2
y' = (-5) / (x - 3)^2

Now, you have the slope of the tangent line, which is -5/(x - 3)^2.

Plug in the x-coordinate of the given point (2, -4) into the derivative to find the slope of the tangent line at that point:

m = -5/(2 - 3)^2
m = -5/1
m = -5

So, the slope of the tangent line at the point (2, -4) is -5.

Use the point-slope form of a linear equation to find the equation of the tangent line:

y - y1 = m(x - x1)

Plug in the values of (x1, y1) = (2, -4) and m = -5:

y - (-4) = -5(x - 2)

Simplify the equation:

y + 4 = -5x + 10

Isolate y:

y = -5x + 10 - 4

Further simplify:

y = -5x + 6

So, the equation of the tangent line to the curve represented by y = (x + 2)/(x - 3) at the point (2, -4) is:

y = -5x + 6

right?

[mystic fern]

holy shit thats a lot, but i know thats the correct answer (back of textbook)

I just didnt even know where to get there

[tardy radish]

Damnnn

[mystic fern]

exactly

Im still lost on the first step, I dont think we have gone over that rule

[tardy radish]

This is tha fcking good full answer

[mystic fern]

I dont want the answer, I want to learn how

[tardy radish]

If he knows the basics of derivative

He can solve it

[mystic fern]

.close

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[alpine sable]

Hello can someone tell me how I would do this problem? like the steps i know you take the derivative and so on but idk whats next

[serene junco]

I think you probably have a formula for arc length of a parametric curve?

[alpine sable]

my problem is when i take the derivative I dont have t anymore so idk where to plug in

these limits

[serene junco]

the derivative is still a function in terms of t, it just happens to be a constant function

$\int_a^b \sqrt{x'(t)^2 + y'(t)^2 + z'(t)^2} dt$

[ocean seal]

tatpoj

[serene junco]

and yes, x'(t), y'(t), and z'(t) are all constant in this case

but that kinda just makes it easier, doesn't it?

[alpine sable]

so like that ?

with the sqrt and square

[serene junco]

just -1, -5, and 4 are fine

just like how you can have f(x) = 5

you can have x'(t) = -1

[alpine sable]

so where would i plug in -3, and 2 ?

[serene junco]

they're the bounds, a and b

[serene junco]

in this formula

[alpine sable]

k imma try it

[serene junco]

@alpine sable feel free to ping if you're stuck or anything

[alpine sable]

thanks yea im stuck

so i did the derivative

[serene junco]

can you show me where you're at?

[alpine sable]

ye i gotta do a new question tho since i messed up give me like a sec

[serene junco]

ok lol

[alpine sable]

What should I do from here ?

[serene junco]

don't write 2(t), etc

that's why you're getting confused

2 is not the name of a function

x'(t) just happens to be equal to 2 for all values of t

it's a constant function

x'(t) = 2

[alpine sable]

oh k

[serene junco]

just sqrt(2^2 + 3^2 + (-1)^2)

[serene junco]

yep so now

$\int_1^5 \sqrt{14} \ dt$

[ocean seal]

tatpoj

[alpine sable]

i got 1/2(14)^3/2

[serene junco]

sqrt(14) is just a constant

like, if you integrated 5, you'd get 5x, right?

same thing, just a different constant

[alpine sable]

oh yea you right

its sqrt14x

[serene junco]

yep, just keep that x out of the sqrt sign lol

[alpine sable]

or t

[serene junco]

oh, t, yeah

[alpine sable]

k so it becomes tsqrt14

[serene junco]

yep, now you just need to evaluate it at the bounds

[alpine sable]

Like that right ?

[serene junco]

yep

[alpine sable]

bet thanks man

do you mind if i stay in this channel i got a few more similar so i can ask if i need help ?

[serene junco]

sure, the bot might close it after a while but you can always open another

[alpine sable]

k thx

[alpine sable]

for this one

is that correct ?

[serene junco]

first part is right, but you can't cancel the sqrt over multiple terms like that

$\sqrt{a+b+c} \neq \sqrt{a} + \sqrt{b} + \sqrt{c}$

[ocean seal]

tatpoj

[serene junco]

oh wait

actually, your derivatives aren't correct either

you need to use the chain rule

[alpine sable]

dam

ight ill try again

[serene junco]

do you see what I mean about the chain rule?

because of the 4t inside the trig functions

[alpine sable]

i think so dam i really forgot so much over the summer

That’s how you do the derivative right ?

[serene junco]

yes but the original coefficients don't disappear

first one should be 52

4 times 13

52cos(4t)

[alpine sable]

k

theres my next steps

[serene junco]

close, but those negative signs get squared too

so all three terms should be positive

[alpine sable]

yep

[serene junco]

(-44)^2 = positive 1936 for instance

this looks really messy, but it's not nearly as bad as it looks lol

[alpine sable]

yea lol

[serene junco]

after you change those -'s to +'s, do you see anything you can do to simplify this before we try integrating?

[alpine sable]

combine the sins ?

[serene junco]

might as well, they're like terms

[alpine sable]

kk

[alpine sable]

is this a trig identity

[serene junco]

the like terms?

[serene junco]

that looks good

[serene junco]

are you asking if this is a trig identity?

[alpine sable]

yea

wouldnt it be 4

[serene junco]

why? does it look like something you recognize?

not sure about 4..

[serene junco]

aha

[alpine sable]

its this trig identity right

[serene junco]

yes, that's true no matter what is in the trig functions, as long as they're the same

sin^2(abc) + cos^2(abc) = 1

no matter what it is, even if it's 4t

[alpine sable]

ohhh

bet so they would = 1

[serene junco]

well, yes, but what you have doesn't exactly look like that

what about the 2704?

[alpine sable]

oh so its 1 * 2704

i think

[serene junco]

yeah, you can factor the 2704 out

2704(cos^2(4t) + sin^2(4t))

[alpine sable]

yep

so we have the sqrt of 2704

[serene junco]

yep

[alpine sable]

=52

[serene junco]

(just don't forget you haven't actually integrated yet)

[alpine sable]

integrated is 52t

[serene junco]

yea

[alpine sable]

nice

alright imma try this next one

i think i got it down

[serene junco]

nice 👍

[alpine sable]

i basically got it right

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

do you know how i would do this one ?

.close

[lone heart]

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[uneven isle]

im not really sure where to even start this question

[blissful whale]

It might help to identify a regular n gon

[uneven isle]

what do u mean by that?

like the dimensions>

oh i see what u mean

[blissful whale]

There is a regular 17 gon

I have not thought it to the end yet but it seems very useful

Actually you can also find 2 other regular n gons

[uneven isle]

u saying polygon made me realise about its diagonals

i mean this yielded what they wanted but im not sure if its the intended way

[blissful whale]

I don't think there are many other ways.

Also the whole fun in mathematics is to come up with your own solutions, right?

[uneven isle]

yeah thats true

[blissful whale]

Now let's see with R

[uneven isle]

hmm

im gonna try similar triangles and see if that gives me the height

[blissful whale]

Isn't R = r + sqrt(2)?

[uneven isle]

yep

and i think i can express height using ratio of similar triangle

[blissful whale]

I think (ii) is just algebra with r and R expression.

[uneven isle]

oh righto, getting side tracked trying to find tan theta for R as well

ah ok

that just expands out nicely to it

part iii is easy since itsj ust differentiating without any twists thankfully

thx for the help 🙏

.close

[lone heart]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hot trail]

i believe i should be correct?

[solemn juniper]

calculations aside, it asks for at least 3 sig figs

this channel is taken, you'll have to go somewhere else

!help

[lone heart]

Please read #❓how-to-get-help